对于任意矩阵A,证明如果(A^H)Ax=(A^H)Ay,则有Ax=Ay.(A^H为A的共轭转置)

问题描述:

对于任意矩阵A,证明如果(A^H)Ax=(A^H)Ay,则有Ax=Ay.(A^H为A的共轭转置)
请教如何证明.

以下用A*表示A的共轭转置
A*Ax=A*Ay => A*A(x-y)=0
=>(x-y)*A*A(x-y)=0
=>[A(x-y)]*A(x-y)=0
=>A(x-y)=0
=>Ax=Ay